207,398 research outputs found

    Shortest path or anchor-based route choice: a large-scale empirical analysis of minicab routing in London

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    Understanding and modelling route choice behaviour is central to predicting the formation and propagation of urban road congestion. Yet within conventional literature disagreements persist around the nature of route choice behaviour, and how it should be modelled. In this paper, both the shortest path and anchor-based perspectives on route choice behaviour are explored through an empirical analysis of nearly 700,000 minicab routes across London, United Kingdom. In the first set of analyses, the degree of similarity between observed routes and possible shortest paths is established. Shortest paths demonstrate poor performance in predicting both observed route choice and characteristics. The second stage of analysis explores the influence of specific urban features, named anchors, in route choice. These analyses show that certain features attract more route choices than would be expected were individuals choosing route based on cost minimisation alone. Instead, the results indicate that major urban features form the basis of route choice planning – being selected disproportionately more often, and causing asymmetry in route choice volumes by direction of travel. At a finer scale, decisions made at minor road features are furthermore demonstrated to influence routing patterns. The results indicate a need to revisit the basis of how routes are modelled, shifting from the shortest path perspective to a mechanism structured around urban features. In concluding, the main trends are synthesised within an initial framework for route choice modelling, and presents potential extensions of this research

    A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems

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    In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to end-point and running state constraints. Building on our previous work, we combine the classical method of needle-variations from geometric control theory and the metric differential structure of the Wasserstein spaces to obtain a maximum principle stated in the so-called Gamkrelidze form.Comment: 35 page

    Transport optimization on complex networks

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    We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the maximum node betweenness with as little path lengthening as possible. We show that by using this optimal routing, a network can sustain significantly higher traffic without jamming than in the case of shortest path routing. A formula is proved that allows quick computation of the average number of hops along the path and of the average travel times once the betweennesses of the nodes are computed. Using this formula, we show that routing optimization preserves the small-world character exhibited by networks under shortest path routing, and that it significantly reduces the average travel time on congested networks with only a negligible increase in the average travel time at low loads. Finally, we study the correlation between the weights of the links in the case of optimal routing and the betweennesses of the nodes connected by them.Comment: 19 pages, 7 figure

    Environment-assisted analog quantum search

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    Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in presence of an idealized fully-engineered bath. However, it is not clear, in general, what performance can be achieved by NISQ when internal bath degrees of freedom are not controllable. In this work, we consider the task of quantum search of a marked node on a complete graph of nn nodes in the presence of both static disorder and non-zero coupling to an environment. We show that, given fixed and finite levels of disorder and thermal fluctuations, there is an optimal range of bath temperatures that can significantly improve the success probability of the algorithm. Remarkably for a fixed disorder strength σ\sigma, the system relaxation time decreases for higher temperatures within a robust range of parameters. In particular, we demonstrate that for strong disorder, the presence of a thermal bath increases the success probability from 1/(nσ2)1/(n \sigma^2) to at least 1/21/2. While the asymptotic running time is approximately maintained, the need to repeat the algorithm many times and issues associated with unitary over-rotations can be avoided as the system relaxes to an absorbing steady state. Furthermore, we discuss for what regimes of disorder and bath parameters quantum speedup is possible and mention conditions for which similar phenomena can be observed in more general families of graphs. Our work highlights that in the presence of static disorder, even non-engineered environmental interactions can be beneficial for a quantum algorithm

    Route Planning in Transportation Networks

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    We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

    Light in Power: A General and Parameter-free Algorithm for Caustic Design

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    We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transports exactly the light emitted by the source onto the target. We first propose a general framework and show that eight different optical component design problems amount to solving a light energy conservation equation that involves the computation of visibility diagrams. We then show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power diagram with a planar or spherical domain. This allows us to propose an efficient and fully generic algorithm capable to solve these eight optical component design problems. The support of the prescribed target illumination can be a set of directions or a set of points located at a finite distance. Our solutions satisfy design constraints such as convexity or concavity. We show the effectiveness of our algorithm on simulated and fabricated examples

    VirtFogSim: A parallel toolbox for dynamic energy-delay performance testing and optimization of 5G Mobile-Fog-Cloud virtualized platforms

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    It is expected that the pervasive deployment of multi-tier 5G-supported Mobile-Fog-Cloudtechnological computing platforms will constitute an effective means to support the real-time execution of future Internet applications by resource- and energy-limited mobile devices. Increasing interest in this emerging networking-computing technology demands the optimization and performance evaluation of several parts of the underlying infrastructures. However, field trials are challenging due to their operational costs, and in every case, the obtained results could be difficult to repeat and customize. These emergingMobile-Fog-Cloud ecosystems still lack, indeed, customizable software tools for the performance simulation of their computing-networking building blocks. Motivated by these considerations, in this contribution, we present VirtFogSim. It is aMATLAB-supported software toolbox that allows the dynamic joint optimization and tracking of the energy and delay performance of Mobile-Fog-Cloud systems for the execution of applications described by general Directed Application Graphs (DAGs). In a nutshell, the main peculiar features of the proposed VirtFogSim toolbox are that: (i) it allows the joint dynamic energy-aware optimization of the placement of the application tasks and the allocation of the needed computing-networking resources under hard constraints on acceptable overall execution times, (ii) it allows the repeatable and customizable simulation of the resulting energy-delay performance of the overall system; (iii) it allows the dynamic tracking of the performed resource allocation under time-varying operational environments, as those typically featuring mobile applications; (iv) it is equipped with a user-friendly Graphic User Interface (GUI) that supports a number of graphic formats for data rendering, and (v) itsMATLAB code is optimized for running atop multi-core parallel execution platforms. To check both the actual optimization and scalability capabilities of the VirtFogSim toolbox, a number of experimental setups featuring different use cases and operational environments are simulated, and their performances are compared

    London's congestion charge

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    On 17 February 2003, one of the world's largest and most ambitious plans to tackle urban congestion began, with the introduction of a congestion charge for central London. It is hoped that this £5 daily charge for many vehicles entering the Inner Ring Road charging zone will significantly reduce the level of congestion faced by those travelling into and out of central London both by private and by public transport. In 2001, almost 1.1 million people entered central London during the morning peak hours of 7.00a.m.-10.00a.m.,1 of whom around 150,000 (13.7%) used private transport. Whilst the total number of people entering during the morning rush hour has scarcely changed since 1991, there has been a small shift towards public transport: in 1991, 16.8% of people used private transport. Nevertheless, average traffic speeds in central London have fallen slightly over the last decade, with the average morning peak-period traffic speed for 2000-03 just 9.9 mph, compared with a peak of 14.2 mph in 1974-76. During the evening rush hour, average speeds are even slower, at just 9.6 mph. In evidence to the House of Commons Transport Committee,3 David Begg of the Commission for Integrated Transport argues that around 40% of the total national level of congestion occurs in Greater London. Transport for London suggests that "there are now no longer any "peaks" or "off-peaks" of traffic volume between 7am - 6.30pm" and states that there are now on average three minutes of delay for every mile that a vehicle travels inside the charging zone. This Briefing Note aims to provide a guide to the workings of the London congestion charge. We begin in Section 2 by describing the economic case for congestion charging, showing why congestion can be thought of as an urban example of the well-known overuse of common resources to which there is free access (the so-called "tragedy of the commons"). In Section 3, we move on to look at the details of the proposed charge for London, examining how it fits in with the economic framework we develop and discussing some of the work that has already been carried out to try to predict the likely effects of the charge. Section 4 looks briefly at the issue of what may happen with the projected net revenues from the charge, which are legally bound for the first 10 years to be spent on transport within Greater London. In Section 5, we discuss some of the empirical evidence regarding transport in London and present evidence on the potential distributional effects of the congestion charge, since one of the oft-cited criticisms of charging is that it will impact upon the poorest most severely. Section 6 goes on to look at the experience of congestion charging elsewhere around the world
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